This is the bit I don't understand. Is the founder/investor essentially holding everyone else to ransom in such a situation, and saying they'll allow the company to go bust if the other participants don't accept a 2/3 cut in their voting power?

In this sort of scenario nobody is being held hostage. The situation is that more money is needed to keep the company operating, there are three ways of getting money, revenue from products, a loan, and selling equity (stock).

Generally revenue isn't a real choice, if it was there then the question wouldn't come up. A loan is trickier, a large loan wants some sort of collateral and if you don't have assets that the lender would take as collateral you are looking at an extortionate interest rate if you can get a loan at all. Worse it adds a re-payment schedule that adds to the burn rate. That leaves selling stock.

So how much is the company "worth?" and what percentage of it would an investor want to buy in order to participate? These are fuzzy numbers, you can say "well sales are X and as a multiple of sales its worth Y" or "the addressable market is Q and these guys capturing 10% would be worth P" but really it comes down to if you believe or don't believe the business is a going concern. It is the place startups go to die, because if they can't convince someone to trade dollars for stock, the next step is bankruptcy.

But if someone is willing to invest they will do so "on their terms" which is to say they will give the conditions under which they will invest. They write this out formally in something called a term sheet. It talks about shares outstanding before the transaction, the transaction itself, and the resulting ownership percentages and valuation post transaction.

So nobody steps forward, next step is bankruptcy. Someone does step forward, well now you have a choice.

A lot of funding agreements have a 'participation right' which basically says Investor A who has 10% has a 'right' to participate in any funding to keep their percentage at 10% or sometimes 10% of the round. So in our example Founder B says I'm setting the terms at $5/share and I'm buying 2M shares for $10M with a post money valuation of $6.66 per share. Then Investor A is offered a chance to participate at that price, so they figure out how many shares they would buy at $5/share such that their ownership would remain at 10% after the transaction. Or they decline. It is their choice. And they may decline because they think its not a good deal, or they think the company is toast anyway and they have already written off that investment as a loss.

Their choice is same voting power in a non-existent entity (bankruptcy) or 1/3 the voting power in a continuing entity. The latter is better than nothing as they say.

If so, how does a company or a co-founder protect against such tactics? I know about anti-takeover strategies like poison pills and so on in the corporate world, but I wonder whether they are really effective in the early stage rounds.

The board votes on whether or not to do the funding round or turn the company assets over to the creditors (bankruptcy) You protect against this scenario by making sure the company is always more valuable as a going concern than as piece parts. The board can try to negotiate a 'better deal' which is to say reduce the percentage stake the new investor is getting in order to approve it, but if they are not participating then that is not a compelling argument.